ES2961232T3 - Operational control in a seismic source - Google Patents

Abstract

A method of controlling the path in a resonant marine seismic source comprises: controlling the frequency of the source and controlling the path of motion. Controlling the frequency of the source includes: estimating the frequency of the source from its internal state and the state of its environment; deriving a frequency error as the difference between the estimated frequency and the desired trajectory frequency; and bring the frequency error to zero. Controlling the motion path includes: detecting a motion path of the source; deriving a motion path error as the difference between the desired motion path and the detected motion path; and bring the motion trajectory error to zero. (Automatic translation with Google Translate, without legal value)

Description

DESCRIPTION

Operational control in a seismic source

[0001] Priority is hereby claimed for US Application Serial No. 61/929,656, entitled "Operational Control in a Seismic Source", and filed on January 21, 2014, in the name of the inventors Mark Francis Lucien Harper and Joseph Anthony Dellinger.

field of invention

[0002] The present invention relates to marine seismic sources and, in particular, to a control strategy for a frequency-controlled resonant seismic source employing a mechanical oscillator.

Background of the invention

[0003] Seismic prospecting consists of studying underground formations based on the reflection of acoustic waves in said formations. This includes introducing acoustic waves into a natural environment so that they penetrate the earth and travel through underground geological formations of interest. During their journey through the formations, some of their characteristics reflect the waves towards the surface, where they are recorded. The recorded reflections are then studied to obtain information about these formations.

[0004] One type of seismic survey is "marine" seismic survey. The term "maritime" only indicates that prospecting is carried out in or on water. It does not necessarily imply that prospecting is carried out in a saltwater environment. Although a marine seismic survey can be performed in a saltwater environment, such as the ocean, it can also be performed in brackish waters, such as those found in bays, estuaries, and tidal marshes. They can even be carried out in completely fresh waters such as those found in lakes, swamps and swamps.

[0005] There are many types of seismic sources whose designs are usually, to some extent, adapted to the environment in which they are intended to be used. Marine seismic surveys are frequently conducted using what is called a "sweep" source. The term "sweep" comes from the operation of these sources, in which they "sweep" a frequency band during the transmission of the seismic signal.

[0006] A recent advance in marine seismic surveying is the acquisition of "buzz" data, that is, data from a signal generated from a "buzz" source. To "buzz" is to use a non-impulsive controlled frequency source that generates virtually all of its power at a single frequency. Due to practical stability limitations, the source can drift controlled or uncontrolled within a narrow frequency range, typically kept within plus or minus a tenth of an octave around the nominal frequency. This is sometimes called "monochromatic" or "near monochromatic", for example in US Application Serial No. 13/327,524.

[0007] The acquisition of tinnitus can occur in several different ways. For example, stepped hum is a sequential acquisition of hum in which a single source cycles through a set of two or more discrete frequencies, one at a time. The time spent moving from one frequency to another should be very small compared to the time spent on each frequency. Another example, chord hum, is acquisition in which one or more sources hum simultaneously at distinct, discrete frequencies. More information can be found in US Application Serial No. 13/327,524.

[0008] Another relatively recent advance in seismic acquisition is "low frequency" acquisition. Seismic surveying has historically used frequencies in the range of 10-250 Hz for seismic signals due to their suitability in view of the technical challenges inherent in seismic surveying. The term "low frequencies" is understood, within this historical context, as frequencies below which obtaining a sufficient signal-to-noise ratio with conventional sources becomes rapidly more difficult as the frequency decreases (i.e., below about 6-8 Hz).

[0009] An example of a low frequency source that can sweep, or hum, or both sweep and hum, at low frequency is disclosed and claimed in US Patent Application Serial No. 12/995,763, presented on June 17, 2009. This particular source consists of a tunable mechanical resonator that, together with its control system, constitutes a self-excited oscillator. The control system detects the speed of the radiating piston and applies a driving force in the same direction as the detected speed, causing the system to oscillate at or near its natural frequency. That frequency is controlled by varying the stiffness of a gas spring, so that the system can oscillate at a single chosen frequency (i.e., "hum") or over a continuous band of frequencies at a given rate (i.e., "sweep"). "). More information can be found in US Application Serial No. 12/995,763.

[0010] However, a problem with low frequency sources is that the frequency introduces problems that typical conventional seismic frequencies do not pose. One way to solve these problems is through exact and precise control of the operation of the source. For example, one type of control is known as frequency stability control, in which the operation of the source is controlled to help stabilize the frequency at which it emits seismic signals.

[0011] US Patent Application No. 12/980,527 (US2011162906) discloses an oscillating piston marine seismic source with a control system that allows the frequency to be adjusted. The source comprises a solenoid that includes a position sensor and thus allows the control system to measure and detect the axial position of a compression piston. The application discloses that the application of a speed-dependent force can be achieved using a simple feedback system from the position sensor to adjust the position of the piston.

[0012] Seismic sources, such as those presented in the aforementioned applications, are suitable for the intended purpose. However, the technique is always susceptible to improvements or alternative approaches, procedures and configurations. Therefore, the seismic source described herein will be well received by the art.

BRIEF DESCRIPTION OF THE DRAWINGS

[0013] The accompanying drawings, which are incorporated and constitute a part of this specification, illustrate embodiments of the description and, together with the description, serve to explain the principles of the invention. In the Figures:

Figure 1 shows a resonant marine seismic source with which the described control technique can be used.

Figure 2 illustrates a particular control system, by which the marine seismic source of Figure 1 can be controlled in accordance with the currently disclosed trajectory control technique.

Figure 3 conceptually represents an exemplary marine seismic survey using the marine seismic source of Figures 1 and 2.

Figure 4 illustrates how the source of Figure 1 is controlled by the control system of Figure 2 to stabilize the frequency of the source during acquisition.

Figure 5 illustrates an example of operating logic for a portion of the frequency stabilization. Figures 6A and 6B illustrate the trajectory control procedure of the present disclosure.

Figure 7 illustrates an equivalent circuit of a single degree of freedom mechanical resonator representative of a low-frequency resonant marine seismic source.

Figure 8 is a graph of the force necessary to control the path of a resonant source.

Figure 9 shows force versus displacement plots for a simple harmonic oscillator before and after frequency stabilization.

Figure 10 shows the operation of the trajectory control procedure and the frequency stabilization procedure for the simple harmonic oscillator of Figure 9.

DESCRIPTION OF THE EMBODIMENTS

[0014] Reference will now be made in detail to the present embodiment or embodiments (illustrative embodiments) of the invention, an example of which is illustrated in the accompanying drawings. Wherever possible, the same reference numerals will be used throughout the drawings to refer to the same or similar parts.

[0015] The currently disclosed trajectory control technique is a control strategy for a frequency-controlled resonant marine seismic source employing a mechanical resonator. Since the marine seismic source is "resonant", it will tend to oscillate naturally at its resonant frequency. The marine seismic source includes an excitation solenoid that injects energy into this oscillation to help overcome, for example, friction and radiation losses. It also includes a solenoid, or solenoids, that control the frequency of its resonance, hereinafter referred to as frequency control technique. However, the amplitude and frequency of the acoustic output of the marine seismic source can vary unintentionally due to both changes in the environment, such as hydrostatic pressure, and changes in the internal state of the source, such as its temperature. internal. This unintentional variation can be detrimental for certain types of seismic surveys.

[0016] Accordingly, the currently disclosed trajectory control technique applies trajectory control to maintain the amplitude and frequency of the acoustic output of the marine seismic source very close to its target values. In this context, "path control" controls the movement of a mechanical oscillator so that it follows a desired path over time. "Path" in this case means the precise movement of the moving part or parts of the oscillator. By "motion" we mean the position, or speed, or acceleration of the parts depending on what is most convenient to detect and control under a series of conditions.

[0017] These conditions may vary depending on the application and, therefore, will be specific to each one of them. For example, controlled motion must be amenable to detection and control despite unforeseen, time-varying, and disruptive environmental influences that may affect both the amplitude and frequency of the oscillator. Or, the movement must be susceptible to detection and control when the amplitude and frequency that characterize the desired trajectory can vary over time; or where the techniques available for controlling the oscillator consist of a mechanism for varying its frequency and an independent exciting force applied directly to the moving parts to excite their motion; or when the exciter force is small compared to the alternating forces that usually intervene in the oscillator, the exciter may influence, but not totally determine, the movement of the oscillator. Other conditions may be apparent to those skilled in the art who benefit from the present disclosure.

[0018] The trajectory control procedure comprises two feedback loops. The first feedback loop estimates the natural frequency of the oscillator, obtains a frequency error as the difference between the estimated frequency and the frequency of the desired path, and uses the frequency control mechanism to attempt to drive the error signal to zero. the manner well known to those versed in control engineering.

[0019] The second feedback loop detects the motion path of the oscillator, derives an error signal from the difference between the desired and sensed paths, and applies a control force through the exciter that attempts to drive the error signal to zero. in the manner well known to those versed in control engineering.

[0020] Returning to the oscillation of the marine seismic source, it can be nonlinear or linear. If the oscillation is nonlinear and the desired trajectory is that of a linear oscillator, the control technique may have the effect of linearizing the behavior of the oscillation. In the illustrated embodiments this is also a high Q resonator, which is a resonator in which a minimum amount of energy input is required to maintain oscillation (for example, the resistive impedance in the resonator, due to friction, viscosity, etc., is much less than the impedance of the spring stiffness at the resonance frequency).

[0021] In document U.S. 12/995,763 a suitable marine seismic source is disclosed and claimed with which the control technique described can be used. To better illustrate and promote understanding of the disclosed trajectory control technique, the present disclosure will now discuss its application to this particular marine seismic source. In the U.S. document A complete description of its construction and operation can be found in 12/995,763, and some modified parts are reproduced herein to reflect the implementation of the present trajectory control technique, as well as frequency stabilization control.

[0022] Turning now to Figure 1, marine seismic source 100 is a high-Q, low-frequency, resonant source. This particular source can be used in both sweep and hum acquisition. It includes a radiating piston 105 on the order of a few meters in diameter supported by a variable gas spring 165 containing gas spring spaces 110a, 110b each with a fixed mass of gas. The resonance frequency of the source is controlled by the relationship between the mass of the moving assembly 105, 125, 130, 120b (including the mass of the fluid 115, typically seawater, entrained in the movement of the piston 105) and the combined stiffness of the variable gas spring 165 and the gas contained within the housing 170. The gas pressure in the spring is maintained at levels for which the natural frequency of the piston 105 loaded by the fluid 115 is in the seismic band and can be as low as 0.5 Hz.

[0023] The piston 105 receives an initial displacement and begins to oscillate. Its oscillations are sustained by a solenoid 240 (shown in Figure 2), composed of an electric linear motor coil 120a, a magnetic rod 120b and a position sensor 255 (also shown in Figure 2). The drive signal of the solenoid 240 is obtained from the speed of the piston 125 through a speed or displacement sensor in accordance with the present control technique. The marine seismic source 100 sweeps its frequency by gradually compressing the gas in the spaces of the gas spring 110a, 110b so that the variable gas spring 165 becomes more rigid. The rigidity increases both by increasing the pressure and by reducing the length of the gas spring spaces 110a, 110b. This double effect allows large changes in stiffness to be produced and, therefore, the marine seismic source 100 to operate at a minimum of three octaves of frequency.

[0024] More specifically, the marine seismic source 100 of Figure 1 is submerged in water 115. A radiating piston 105, on the order of a few meters in diameter, is attached to a shaft 125 that is free to move vertically. Behind the radiating piston 105, a secondary piston 130 is also attached to the shaft 125 and divides the gas inside the gas spring cylinder 133 into two volumes 110a, 110b. The upper end of the space 110a is closed by a tertiary piston 132 attached to a yoke 140.

[0025] The yoke 140 is in turn attached to a linear solenoid 145, which has a very high mechanical impedance compared to the mechanical impedance of the gas spring 110a, 110b. The solenoid 145 incorporates a position sensor (not shown) that allows a control system to measure the position of the solenoid 145 at any time and stiffen its movement using active feedback in a manner well known to those skilled in industrial control systems. . The position of the tertiary piston 132 will be controlled by the solenoid 145 and, due to the active rigidity, will not be affected by pressure changes in the volume of the gas spring 110a resulting from the oscillations of the radiating piston 105.

[0026] The solenoid 145 is driven by an electric motor 150 through a drive belt 155. Within and supported by the yoke 140 is an electric linear motor coil 120a. A magnetic rod 120b is guided through the coil 120a by plain bearings (not shown) and is attached to the upper end of the shaft 125. An electric linear motor can be used because it has low mechanical impedance and therefore does not limit or prevents the movement of the mobile assembly 105, 125, 130, 120b. The linear motor incorporates a position sensor (not shown) that allows a control system to measure the relative position of the rod 120b and the coil 120a of the solenoid, at any time, in a manner well known to those skilled in the art of systems. industrial control.

[0027] Figure 2 illustrates a particular control system 200 by which the marine seismic source of Figure 1 can be controlled in accordance with the currently disclosed trajectory control technique. A master controller 205 communicates with two single-axis servo controllers 211, 210 via serial communications links 215, 220. It also communicates with storage 222 via a communications link 208 as described below.

[0028] The servo controller 211 controls the high impedance solenoid 225 composed of the solenoid 145, the motor 150 and the transmission belt 155, through the transmission lines of the motor 230. The extension of the solenoid 145 is fed back from a sensor internal 245 (for example, a shaft encoder in its motor 150) to the servo controller 211 via the feedback cable 252. Likewise, the servo controller 210 controls the low impedance solenoid 240, partially composed of the coil 120a and the rod 120b, through the motor transmission lines 250. The position of the radiating piston 105 is transmitted to the servo controller 210 from a position sensor 255 coupled to the radiating piston 105, which may be, for example, a linear variable differential transformer.

[0029] The master controller 205 is used to download the control programs 260, 265 to the servo controllers 211, 210. The program 260 downloaded to the servo controller 211, when started, can cause the high impedance solenoid 225 to execute an extension desired which may consist, for example, of a brief initial phase of high acceleration, an extension phase at constant speed, a subsequent brief deceleration phase in which the solenoid 225 is brought to rest, a delay which may be, for example , ten seconds long, and a return to start phase in which the solenoid extension returns to its initial value and the program ends its execution. The total time interval between initiation and return to the initial extension value may be fixed and may be denoted as T.

[0030] The program 265 downloaded to the servo controller 210, when started, can cause the low impedance solenoid 240 to supply an initial impulsive force to the piston rod 125 and then can monitor the movement of the radiating piston 105 through of the sensor 255 and causing the solenoid 240 to apply a fixed level of force in the direction of movement, thereby effecting "bang-bang" control in a manner well known to those skilled in the art of control system design. The force can then be reduced to zero and the program 265 can terminate after a time interval after initiation also equal to T.

[0031] In normal operation, the master controller 205 can cause the programs 260, 265 downloaded to the controllers 211, 210 to start executing simultaneously. The combined effect will then be to cause the system to perform a frequency sweep as described above.

[0032] The master controller 205 also implements the control technique described herein according to the application 270 residing in the storage 222. In addition to sending control signals to the high impedance solenoid 225 and the low impedance solenoid 240 , also receives feedback from them through links 215, 220. The master controller 205 acts on this feedback and according to the application program 270 controls the trajectory of the piston as described below.

[0033] The control system 200 is located on or within the seismic source 100 of Figure 1 in the illustrated embodiment. However, this is not necessary for the practice of the control technique disclosed herein. Those skilled in the art, with the benefit of this disclosure, will appreciate that some parts of the control system 200 could be located elsewhere. For example, in alternative embodiments, it could be located on the tow vessel and signals could be transmitted back and forth via an umbilical.

[0034] Those skilled in the art, with the benefit of this disclosure, will also appreciate that the aspect of the currently disclosed trajectory control technique described above is computer implemented. Figure 2 conceptually represents selected portions of the hardware and software architecture of the control system 200 that are relevant to the implementation of the control technique disclosed herein. The disclosed trajectory control technique allows for wide latitude in the implementation of these parts and the control system 200 may include software and hardware not disclosed herein.

[0035] For example, the master controller 205 may be any suitable electronic processor or set of electronic processors known in the art. Those skilled in the art will appreciate that some types of electronic processors will be preferred in various embodiments depending on specific known implementation details. Factors such as processing power, speed, cost and power consumption are often found in the design process and will be very specific to each application. Due to their ubiquity in the art, such factors will be easily reconciled by those skilled in the art who have the benefit of this disclosure.

[0036] Those skilled in the art, with the benefit of this disclosure, will therefore appreciate that the master controller 205 can theoretically be an electronic microcontroller, an electronic controller, an electronic microprocessor, an array of electronic processors, or a circuit Application Specific Integrated Circuit ("ASIC") or a Field Programmable Gate Array ("FPGA"). Some embodiments may even use some combination of these types of processors.

[0037] Storage 222 may include a hard drive and/or random access memory ("RAM") and/or removable storage. Storage 222 is encrypted with a number of software components, including programs 260, 265, and application 270. It may also be encrypted with other software not shown. For example, it may include test software so that the marine seismic source 100 can be interrogated and its settings tested before or during deployment. Other types of software, such as an operating system, not shown, may also reside on storage 222.

[0038] Furthermore, there is no requirement that the functionality of the control system 200 described above be implemented as disclosed. For example, application 265 may be implemented in some other type of software component, such as a daemon or utility. The functionality of the application 270 does not have to be aggregated into a single component and may be distributed across two or more components.

[0039] Note that some portions of the detailed descriptions herein are presented in terms of a software-implemented process involving symbolic representations of operations on data bits within a memory in a computing system or computing device. These descriptions and representations are the means used by subject matter experts to most effectively convey the essence of their work to other subject matter experts. The process and operation require physical manipulations of physical quantities that will physically transform the particular machine or system in which the manipulations are performed or in which the results are stored. Typically, but not necessarily, these quantities take the form of electrical, magnetic, or optical signals capable of being stored, transferred, combined, compared, and otherwise manipulated. It has sometimes been convenient, mainly for reasons of common usage, to refer to these signals as bits, values, elements, symbols, characters, terms, numbers or the like.

[0040] However, it must be taken into account that all these and similar terms must be associated with the appropriate physical quantities and are nothing more than convenient labels applied to said quantities. Unless specifically indicated or otherwise apparent, throughout this disclosure, these descriptions refer to the action and processes of an electronic device, which manipulates and transforms data represented as physical quantities (electronic, magnetic or optical) within the storage of some electronic device in other data similarly represented as physical quantities within the storage, or in transmission or display devices. Examples of terms designating such a description are, without limitation, the terms "processing", "computation", "calculation", "determination", "visualization" and the like.

[0041] Furthermore, the execution of the software functionality transforms the computing device on which it is executed. For example, the acquisition of data will physically alter the contents of the storage, as will the subsequent processing of that data. The physical alteration is a "physical transformation" in the sense that it changes the physical state of the storage of the computing device.

[0042] Note also that software-implemented aspects of the invention are typically encoded on some type of program storage medium or, alternatively, implemented on some type of transmission medium. The program storage medium may be magnetic (for example, a floppy disk or hard drive) or optical (for example, a compact disc read-only memory, or "CD ROM"), and may be read-only or random access. Likewise, the transmission medium may be twisted pairs of wires, coaxial cable, optical fiber, or some other suitable transmission medium known in the art. The invention is not limited by these aspects of any given implementation.

[0043] The trajectory control technique described above is implemented during acquisition in a marine seismic survey to control the amplitude and frequency of the seismic signals emitted by the marine seismic source. The survey design may be carried out in accordance with conventional practice and will normally include one or more towing vessels towing one or more sources. For present purposes, an illustrative embodiment of a source with which the survey can be performed is the marine seismic source of Figure 1-Figure 2. The survey may also include one or more ocean bottom cables such as those known in The technique.

[0044] Consider, for example, the marine seismic survey 300 of Figure 3. The survey 300 includes a vessel 305 from which the marine seismic source 100 is deployed and towed. The marine seismic source 100 is towed through the water 115 as planned in the survey design at a depth that depends in part on its frequency. A plurality of receivers 310 (only one indicated) are deployed from survey vessels (not shown). Some marine surveys tow receiver arrays 310 mounted on streamers grouped into streamer arrays in a manner not shown. However, the illustrated embodiment deploys the receivers on the seabed 316 as part of ocean floor cables 320 (only one is indicated).

[0045] Once the deployed marine seismic source 100 is heated, the towing vessel 305 tows it following the sail lines required by the design. While the marine seismic source 100 is towed, it emits seismic acoustic signals represented by beam 325. In the illustrated embodiment, these may be sweep or hum seismic signals, as required by the survey design. The acoustic signals propagate through the water 115 until they encounter the seabed 316. A part of the signal is reflected from the seabed 316 to the sea surface, as represented by the beam 330, and another part continues to propagate through the subsurface 315, as indicated by beam 335. Periodically, the acoustic signal will encounter reflectors, such as reflector 340, and a portion will be reflected back to the receivers 310 as indicated by beam 345 and a portion will continue until the energy of the signal to dissipate beyond what the receivers 310 can detect. A part of the acoustic signal can also return to the bottom or surface of the sea by mechanisms other than reflection, such as refraction or rotation (the so-called "dip wave").

[0046] The currently disclosed trajectory control technique operates during the generation and emanation of seismic acoustic signals. The frequency stabilization and trajectory control loops are described in more detail below.

[0047] Turning now to Figure 4, a flow chart 400 illustrates how the source of Figure 1 is controlled by the control system of Figure 2 to stabilize the frequency of the source during acquisition. In flowsheet 400, nominal sweep design parameters are used both to initialize source 420 and user adjustable parameters in frequency stabilization (at 440). These parameters are determined during the design of the aforementioned survey and can be arrived at conventionally. Frequency stabilization (at 440) may be implemented, for example, by application 270 residing on the local or remote hard drive or within some other type of storage device (e.g., storage 222 shown in Figure 2). and executed by the master controller 205. The master controller 205 monitors (at 450) the operational seismic source 100, calculates the necessary disturbance (at 500) and updates the internal configuration of the marine seismic source 100 (at 430) as desired to adjust the emitted frequency back to the nominal frequency.

[0048] Referring again to Figure 1, in operation, the radiating piston 105 moves with displacement x against the pressure Pext of the external seawater 115. The device is shown in equilibrium, x = 0, so that the pressure inside the device it is also Pext. The radiating piston 105 is attached to a shaft 125 passing through a variable gas spring 165 comprising two gas volumes 110a, 110b, confined by a compression piston, 132. The variable gas spring 165 are both gas spring volumes 110a, 110b defined by the pistons 132, 130, and the cover 129 and their respective seals. Attached to shaft 125 is a piston 130 that moves freely in the direction of shaft 125, along with the shaft, within gas spring 165. Seals (not shown) around the perimeter of piston 130 prevent movement of gas around the piston 130, creating two sealed compartments on each side, 110a, 110b. A compression piston 132 mobile along the axis of the shaft 125, also sealed around its entire perimeter, allows the length of the gas spring 110a, 110b and, therefore, its rigidity to be varied. The length of the gas spaces 110a, 110b, being equal to the total distance between the nearest faces of the compression piston 132 and the cap 129 minus the thickness of the secondary piston 130, is indicated as V. The pressure inside the compartments 110a, 110b of the compression piston in equilibrium is Ps.

[0049] As discussed above, the marine seismic source 100 tends to oscillate at a natural frequency determined by parameters such as the position of the compression piston 132, the gas pressures within the spaces 110a, 110b and the interior of the casing. 170 inside the device, the external pressure of the Pext water (and therefore the operating depth of the device) and, to a lesser extent, the frictions of the seal and the force and moment of activation of the linear solenoid 240 (shown in the Figure 2) that supplies energy to the oscillations of the radiating piston. The compression piston 132 controls the resonant frequency of the source by simultaneously modifying the equilibrium pressure Ps inside the gas spring and its length.

[0050] To perform a given frequency sweep, the compression piston 132 moves to change the period of oscillation as necessary, but otherwise the device is allowed (for the most part) to oscillate at its natural frequency with a amplitude which can be controlled by using the solenoid 120a, 120b, as already described. Typically, the required trajectory of piston 132 will be calculated before the sweep begins. The default control law of the compression piston, the aforementioned active stiffness, acts to maintain the piston 132 in its precalculated trajectory despite the disturbing forces introduced by the operation of the device. Another control law separately governs the drive solenoid 120a, 120b to supply power to or extract power from the oscillations as needed.

[0051] Thus, for example, following the default control law, the compression piston 132 could be positioned so that it theoretically generates an oscillation at 2.0 Hz, but instead an oscillation occurs at 2.05 Hz because the theory underlying the control law is only an approximation, or the conditions, including the aforementioned gas pressures, do not exactly match the assumptions of the control law calculation. The frequency stabilization loop (430, 450) is designed to minimize this type of error.

[0052] More specifically, it uses active feedback from the compression piston 132 to keep the device much closer in frequency, on average, so that the natural frequency of the device becomes closer to the desired frequency. The feedback loop is used to adjust a controllable parameter in order to minimize the discrepancy between the desired frequency and the natural frequency. In the illustrated embodiment, this is done by adjusting the position of the compression piston 132.

[0053] The controllable parameter in this embodiment is a disturbance P that can be applied to the pre-calculated default position of the compression piston (DSPP). The natural frequency (f) of the source depends on the length of the gas spring (/) and we will indicate it by writing f(í). Note that the natural frequency also depends on many other factors, including the gas pressure in spaces 110a, 110b of Figure 1 and the pressure Pext of the external fluid, but these dependencies are omitted for the sake of brevity. Now suppose that a discrepancy Af = fi(l) - fe(l) occurs between the predicted natural frequency, which we will denote as f(í), and the estimated frequency fe(í). This could occur, for example, as a result of a change in temperature of the gas in spaces 110a, 110b. We wish to correct fe(í) closer to f(í) by changing the length of the gas spring / = DSPP P. This can be achieved by the following simple iterative scheme. From the knowledge of the dynamics of the system = dfe(. 0 /

we calculate the rate of change: e to correct the discrepancy

The disturbance P to the predetermined position of the compression piston DSPP is now corrected by an amount A/ to a new value P' as follows:

[0054] In this case a is a value of the stabilization factor between 0 and 1, set by the user according to principles well known to those skilled in the field of control system design.

[0055] The quantity e can be calculated as follows for a device such as that of Figure 1. In this example it will be assumed that the gas inside the spring behaves adiabatically on the time scale of one period of the resonance, i.e. that a quarter period of the gas spring piston oscillations is too short for significant thermal energy transfer to occur between the metal structure and the gas. The stiffness of the gas spring at small displacements can then be determined, as well as the change in length required to counteract a change in the estimated natural frequency.

[0056] In this example, to displace the gas spring piston a distance x from the equilibrium position x = 0, the gas spring piston would have to apply a force given by the equation:

where,

x is the displacement of the gas spring piston from the center position,

ps is the gas pressure inside the variable gas spring when the piston is at rest,

This is the piston area of the gas spring,

l is the total length of the gas space of the gas spring (i.e. the sum of the lengths on both sides of its piston), and,

And it is the adiabatic index (ratio of the main specific heats) of the gas. Differentiating with respect to x and evaluating the result at x = 0, the expression for the spring stiffness for small displacements is obtained:

d£_

k_ 4ypsA s

dx*=0l

When determining the change in stiffness with length (i.e. the position of the compression piston), in this embodiment the change in gas pressure that this produces must be taken into account. In doing this, it will be useful to make an additional assumption, that on the time scales on which the length of the gas spring changes, the gas is

capable of thermodynamic equilibrium with the metal and, therefore, the partial derivative ' 1 behaves according to Boyle's Law:

dk_dk_dk_dps_-AypsAs4yAsps_k

di ~ di dps di ~ l2 l l ~ ¿l

[0057] To use the above expression to model a control system, according to this embodiment a model of how the stiffness of the gas spring affects the natural frequency is also needed. This model could be obtained as follows: The natural frequency of the system as a whole depends on the moving mass (the radiating piston and everything attached to it, including the shaft and the gas spring piston), the stationary mass (the casing and everything attached to it) and the rigidity of the gas spring. It also depends on the rigidity of the gas in the casing, which contains a third sealed compartment filled with gas. We can model this system as a simple harmonic oscillator formed by two parallel springs between two masses.

[0058] The known formula for the angular resonance frequency of an oscillating system containing two parallel springs between two masses is

In this case,

Úfy

kv is the stiffness dx of the gas inside the casing, where Fv is the force exerted on the piston 105 by the gas inside the casing 170;

m1 is the total mass of the piston 105, the shaft 125 to which it is attached, and anything else attached to the shaft such as the piston 130, and the added mass of water moving with the piston 105;

m2 is the mass of the rest of the source, including the casing 170 and everything rigidly attached to it.

The effect of changing the lengths of the gas springs can be calculated as follows:

In terms of frequency (f) and not angular frequency w

The amount/ ; (or in the previous equations it can be considered identical to this one.

[0059] To include kv in the model, it will be convenient to assume again in this example that the gas behaves adiabatically on the time scale of a quarter period, so that an expression analogous to that for the stiffness of the spring can be used. gas:

where L is an "equivalent length" of the gas space of the casing, equal to its volume V divided by the piston area A. Factor 4 has disappeared because there is only a single gas space.

[0060] Figure 5 contains an illustration of how the above equations could be used in a particular embodiment. In this embodiment, the resonator parameters described above will be determined (at 505) along with the sweep pattern and Af. Some of these parameters may be characteristic of the type of resonator used and others may have to be determined separately for each resonator. Furthermore, in some cases parameters calculable from those identified above could be determined (i.e., a set of parameters should be determined for the resonator from which those identified above can be calculated).

[0061] In this particular embodiment, some of the parameters, including k, kv, and df/dl, identified herein are calculated (at 515, 520). Some of these quantities may only need to be calculated once per survey. Others may have to be determined again with each attempt. For example, if the temperature of the device changes over time, or may need to be continually recalculated during each sweep as the compression pistons move, then the various internal pressures and stiffness values will change as a result. Thus, although Figures 4 and 5 appear to indicate that the calculation of these parameters (at 515, 520) is outside the feedback loop (at 430, 450), it should be understood that, in some cases, several of these quantities could be repeatedly recalculated as the situation requires. An estimated correction is calculated (at 530) and applied (at 540).

[0062] In this example, the default (unaltered) control law (at 420) will be used to determine the initial position of the compression piston. This positioning can be adjusted depending on the type of survey selected (for example, single frequency, narrowband scanning, etc.) and the specific frequencies in question.

[0063] A sweep is performed, according to the designed sweep pattern (at 430). During that sweep, in one embodiment, the actual performance of the resonator will be measured and compared to the desired sweep. According to current technique, this will be done by estimating its natural frequency. In the event that a hum is required, the estimate of the natural frequency will provide a measure of the precision of the sweep and the deviation from it. If the resonator sweeps over a range of frequencies, it will still be possible to determine a deviation from the desired sweep frequencies since, in a sweep over a range, an expected frequency at each time point will be known and can be compared to the frequency estimated natural for that time interval. There are many alternative system state estimation techniques to establish the frequency deviation of the gas piston from the desired frequency. Those with ordinary knowledge in the field will be easily able to devise the same.

[0064] Any such procedure must take into account the effect of the path control loop 650 on the actual frequency of the device. The frequency deviation that must be estimated is the difference between the resonant frequency of the device in the absence of path control (its "natural frequency") and the desired frequency. If the natural frequency estimation procedure is based on the observed frequency of the device, you must estimate and take into account the effect of the trajectory control loop 650. Alternatively you can estimate the natural frequency from the arrangement of the compression piston 132 , the gas spring piston 130, and the gas pressures in the spaces 110a, 110b and within the housing 170.

[0065] Finally, given some measure of the frequency deviation, a setting (at 450) can be determined using the equations set forth above (at 515-530) and the sweep continued.

[0066] As an example, consider some conditions that might be typical for a device; such as, for example, marine seismic source 100 in Figure 1, configured to deliver a 4 Hz hum at an operating depth of 30 meters. In this specific case, the diameter of the radiating piston will be 1.38 meters, the area of the compression piston will be 0.25 m2, and the internal volume of the device will be 8 cubic meters. Using the previous equations, the stiffness can be calculated as follows:

l = 0.66 m (the appropriate value for a 4 Hz resonance);

p = 400,000 Pa (ambient pressure at -30 m depth);

As = 0.25 m2;

A = ^(1.38mV2)2 = 1.50 m2;

V = 8 m3, and,

Y = 1.4 (the adiabatic index of a diatomic gas such as nitrogen).

The above implies that:

k = 8.48 x 105 Nm-1

kv= 1.58 x 105 Nm-1

O well

Note that the above equation can be considered, in a sense, as the translation of a frequency error into a position error, which position error can be adjusted according to the teachings set forth herein.

[0067] For the purposes of this example, this implies that to correct a 5% deviation in frequency (not atypical in this type of testing), the compression piston 132 would have to move about (0.05)(4 Hz) /(5.11 Hz/m) = 0.0392 meters, or about 40 mm. This perturbation should not be too demanding for many systems of interest.

[0068] The frequency stabilization feedback loop just discussed controls the natural resonance of the system to keep it close to the desired frequency. The present trajectory control technique includes an additional feedback control loop that controls the detail of the trajectory, while the frequency feedback control loop, described above, maintains the natural frequency of the marine seismic at the correct frequency, or almost correct. The implementation of this second control loop will now be described with respect to the marine seismic source 100 of Figure 1.

[0069] In this case, the trajectory of the trajectory control refers to the relative displacement of the radiating piston 105 and the housing 170 ("relative trajectory"). The frequency control mechanism consists of modifying the positions of the compression piston 132 at the end of the gas spring 165; and the excitation force is applied through the excitation solenoid 240. The marine seismic source 100 will typically be used cyclically, exactly repeating its desired trajectory with a fixed or nearly fixed period of time between repetitions. In this case, the first control loop described above can detect the frequency error during one cycle and apply the correction by the frequency control mechanism in the next cycle. However, the second control loop will work in real time (i.e. immediately).

[0070] The control mechanism in this case is the control system 200 shown in Figure 2. Note that this is, by way of example and illustration, one of the means by which the operation of the source can be controlled marine seismic 100. As discussed above, the trajectory control procedure is implemented in this embodiment in the application 270 and comprises two sets of two feedback loops.

[0071] Referring now to Figure 6A, the first loop 600 estimates (at 610) the natural frequency of the source. It then obtains (at 620) a frequency error as the difference between the estimated frequency and the frequency of the desired trajectory. It then uses (at 630) the frequency control mechanism to attempt to drive the error signal to zero in a manner well known to those skilled in control engineering.

[0072] Returning to Figure 6B, the second feedback loop 650 detects (at 660) the motion path of the oscillator. It then obtains (at 670) an error signal from the difference between the desired and detected trajectories. Next, a control force (at 680) is applied through the exciter which attempts to drive the error signal to zero in a manner well known to those skilled in control engineering. One way to drive the error signal to zero is to measure the motion error between the desired and detected motions of the oscillator. A control force linearly proportional to the error is then applied. Alternatively, "bang-bang" control can be used: applying a force of constant magnitude in the direction opposite to the error. Other forms of control may be considered by a person skilled in the art.

[0073] The first loop 600 closely follows the procedure disclosed in US Application No. 61/894,729, filed on October 23, 2013, and in US Application No. 14/515,223, filed on October 15, 2014, titled "System and Method for Resonator Frequency Control by Active Squeeze Position Feedback." However, one difference is that the second loop 650 will act to maintain the oscillation at the desired frequency, regardless of the natural frequency of the source. Therefore, if the second loop is in operation, the natural frequency cannot be estimated by directly measuring the period of the oscillations, which is usually the simplest means of estimation.

[0074] An estimation procedure would be to briefly disconnect the second loop, directly measure the natural frequency of the source, use this estimate in box 610, and then reconnect the second loop. Alternatively, the natural frequency of the source can be estimated from measurements of its internal state and the state of the environment. For example, the natural frequency of the source may be tabulated for a variety of pressures, temperatures, operating depths, etc., and based on real-time measurements, the appropriate tabulated value is used as an estimate in box 610. In one embodiment, The frequency error can be estimated indirectly from the history of trajectory errors (Box 675).

[0075] To better understand how the two feedback control loops 600, 650 can be implemented with respect to the marine seismic source 100 of Figure 1-Figure 2, an analytical numerical example will now be provided. This example will demonstrate in particular that the forces required to correct the trajectory (in box 680) depend largely on the natural oscillation frequency of the source (estimated in box 610).

[0076] Consider the source as a simple one-degree-of-freedom oscillator, as illustrated in the equivalent circuit of Figure 7. The mass of the piston m-\ is represented by 720, the mass of the remaining source m2 by 710. The variable constant of the spring is k N/m (730), the viscous resistance is r N/(m/s) (750), and the two masses are excited to relative motion at angular frequency w rad/s with tip speed v m /s by a force of amplitude F, measured in Newton.

[0077] In this context, F is the excitation force applied to the source; w is the angular frequency at which you want the source piston to oscillate; The top speed with which it is desired to oscillate is denoted by v.

[0078] As is known to a person skilled in the field of dynamics, the following relationship between the force F, the frequency w and the properties of the oscillator, expressed in the frequency domain in complex notation, is valid:

F=v(r+i(om

[0079] In this case m is the harmonic mean of the masses m-\ and m2.

[0080] This can be rewritten in terms of the natural frequency W0 of the oscillator:

[0081] From inspection of this equation it is evident that when forced at the natural frequency, an excitation force f = v r will produce a velocity v, and that at any other frequency the force required to produce the, or r<2>- how <2>same speed v will be greater. The force increases as the frequency difference increases. Thus, if it is desired to produce a certain speed v and the available force is limited to Fmax, then the natural frequency W0 must be kept close to the desired frequency w. It is also evident from this equation that the maximum difference between the desired frequency and the natural frequency at which the available excitation force will still be sufficient to produce the desired velocity v depends on Fmax and decreases with increasing m and r.

[0082] Suppose, for illustrative purposes, that a font has the following characteristics:

r = 3000. N/m/s;

v = 2 m/s;

m = 3000 kg; in this case it represents the effective moving mass, typically the harmonic mean of the piston and casing masses;

desired frequency = 2 Hz;

Fmax = 10,000 N;

[0083] Figure 8 shows a graph of the force that would be needed to control the trajectory, as a function of the tuned natural frequency of the source. A horizontal line indicating Fmax is also shown.

[0084] It is evident that the required force increases very rapidly with the frequency error. In this example the natural frequency range of the oscillator must be kept within the range of 1.9 Hz to 2.1 Hz for path control to be effective by controlling the path to be a 2 Hz oscillation with a peak speed of 2 m/s. That is, the path control will not tolerate a frequency deviation greater than 0.1 Hz, or 5% of the desired frequency.

[0085] It will be apparent to those skilled in the art that the forces required are highly dependent on the frequency error A f and therefore the history of the corrective forces applied at 680 can be used at 675 to estimate the natural frequency of the oscillator at 610. In In one embodiment, the corrective forces are applied as follows: Let "fxd" be the control force applied at 680 multiplied by the displacement of the moving assembly 105, 125, 130, 120b with respect to its position averaged over one cycle of oscillation. So, for a simple harmonic oscillator system and a small frequency error, to good approximation, "fxd" averaged over one oscillation cycle will be directly proportional to the 620 frequency error.

[0086] This can be seen as follows: The force versus displacement for a simple harmonic oscillator system follows Hooke's law, F = kx, where "F" is the force applied by the spring, "k" is the constant elasticity of the spring, and "x" is the displacement from the natural length of the spring. If the moving mass obeys this equation despite an error in the spring constant k, which instead of the nominal value k has the value kactual, then the applied path control force Fcontrol must be exactly compensating for the error: F = k x = Fcontrol kactual x, and therefore Fcontrol = (k - kactual) x. Multiplying the control force by the displacement x, we have fxd = Fcontrol x = (k - kactual) x2. Averaged over one oscillation cycle, x2 averages to half its maximum value, and therefore Fcontrol x averaged over one oscillation cycle is proportional to k - kcurrent.

[0087] This allows the difference of the squares of the desired frequency oids and the natural frequency Mnat to be estimated as follows:

[0088] In this case, a superscript bar indicates the average over an oscillation period.

[0089] The natural frequency can then be estimated directly and the control loop 600 can operate by applying this calculation in step 610.

[0090] These calculations are only accurate for a linear oscillator, while the system in Figure 1 constitutes a nonlinear oscillator with a superlinear spring. The previous result will be applied with increasing precision the smaller the oscillations are, since in the limit of infinitesimal movements the system behaves linearly. For finite oscillations, the above equations will only provide approximate results. However, the graph in Figure 8 indicates that trajectory control will be successful for finite errors in the frequency difference, so some degree of error in the estimation and correction of the natural frequency can be tolerated.

[0091] Other embodiments that allow control force 680 to be used to estimate natural frequency 610 and frequency error 620 will be apparent to those skilled in the art. Figures 9 and 10 show a computational numerical example of these interactive control loops in practice. Figure 9A shows the force as a function of displacement for an ideal linear spring with a spring constant k = 1 (910), and for a partially nonlinear spring that becomes stiffer at larger displacements: k = (1 displacement4)/ 10 (920). We build a harmonic oscillator using these two springs, with the mass and initial velocity chosen so that for the linear spring the period of oscillation is 2 seconds and the maximum displacement is 1 meter. Our goal is to use trajectory control to make the nonlinear spring act like the linear one.

[0092] Figure 10A, from 0 seconds (at 1000) to 20 seconds (at 1020), shows how linear and nonlinear oscillators differ in free oscillation. The dotted line shows the motion for the linear spring, and the solid line shows the motion for the nonlinear spring. The main effect of the increase in the stiffness of the nonlinear spring at higher displacements is the slight decrease in the oscillation period. After 20 seconds of free oscillation, a significant phase error has accumulated. Figure 10B shows the trajectory error,the difference between these two cases.

[0093] At 20 seconds (1020) trajectory control loop 2 (650) begins. The applied control force (shown in Figure 10E) is linearly proportional to the velocity error, but is limited in magnitude to 5% of the maximum linear spring force. The trajectory error (Figure 10B) reduces as the control force brings the phase of the oscillation back into alignment with the desired trajectory, but the error does not reach zero. It cannot, because the force needed to completely correct the spring nonlinearity is too large (it is outside the limits of the dotted lines in Figure 9A, which show the maximum force deviation that could be corrected to return to the case ideal 910).

[0094] At 50 seconds (1050) control loop 1 (600) begins, the frequency control. It is allowed to adjust the global stiffness of the spring, but not to correct the nonlinearity of the spring: k = (klinear displacement4)/10, with klinear being the adjustable parameter. Figure 10C shows “fxd”, which represents the calculated control force (before trimming to 5%) multiplied by the displacement. The rate of change of the linear part of the klinear spring constant is proportional to fxd averaged over two-second intervals (but with a maximum forced rate of change). The perturbation of the linear part of the spring constant is applied at the end of each averaging interval (as in box 450). Figure 10D shows how the linear part of the spring constant is quickly adjusted to bring the natural period to the required 2 seconds. The fitted spring is still non-linear, as shown in Figure 9B, with k = 0.937 displacement4/10, but after fitting, the required forces are now small enough that the control force is adequate for the task, and the trajectory error (Figure 10B) is brought almost to zero.

[0095] This simple computational model demonstrates how combined control loops 600 and 650 can produce nearly perfect sinusoidal motion from an oscillator with a strongly nonlinear spring. Those skilled in control theory will be able to conceive of many alternative implementations to the simple examples given here; In particular, control laws may adjust adaptively ("learn"), anticipate corrections based on previous experience, or may include other sources of information, such as measurements of the source environment (e.g., based on temperature, pressure or depth).

[0096] In the embodiment illustrated in Figure 1, the marine seismic source 100 of Figure 1-Figure 2 is deployed for acquisition as in Figure 3 or in a similar manner. During acquisition, the operation of the marine seismic source 100 is controlled by both the frequency stabilization technique illustrated in Figure 4-Figure 5 and the trajectory control of Figure 6. More specifically, the frequency stabilization technique of Figure 4-Figure 5 operates within the trajectory control loop 1 (600) to control the marine seismic source 100 so that it resonates at the correct frequency, or very close to the correct frequency. Once it is resonating at the desired frequency, the trajectory control loop 2 (650) also makes small adjustments to the oscillatory motion.

[0097] That is, path control loop 1 (frequency stabilization) makes large, or "gross", changes in frequency, while path control loop 2 makes small, or "fine" changes in frequency or movement. A small change in frequency, for example, could be 0.1 Hz. Or, a small modification of the movement can change the precise shape of the sweep, for example, to damp unwanted high-frequency harmonics, or perhaps to accentuate a specific harmonic. Therefore, trajectory control loop 2 continually makes small tweaks or adjustments to the motion to keep it closer to a desired nominal trajectory.

[0098] Note the contrast with the operation and control of a terrestrial vibrator. A terrestrial vibrator is an example of a poorly resonant system. The ground vibrator abruptly forces the output of the device, forcing the driving piston to move along a certain path. That is, it forces the radiating piston to move to where it should be without taking into account what its resonance frequency is. However, in marine seismic source 100, the driving solenoid is not powerful enough to force the device to a particular frequency that differs significantly from its natural resonant frequency. Instead, it "tunes" the response that the device already "wants to give" (i.e., its natural resonant frequency).

[0099] Where reference is made herein to a procedure comprising two or more defined steps, the defined steps may be carried out in any order or simultaneously (except where the context excludes that possibility), and the procedure may also include one or more steps that take place before any of the defined steps, between any two of the defined steps, or after all of the defined steps (except where the context excludes that possibility).

[0100] The following patent applications and patents are hereby disclosed by reference to the parties listed and for the stated purposes:

[0101] US Application Serial No. 12/995,763, entitled "Marine Seismic Source", filed June 17, 2009, in the name of inventors Martin Thompson and Mark F. L. Harper, published April 14 2011, as US Patent Publication 2011/0085422, and commonly assigned herein for its teachings of the structure and operation of an illustrative low-frequency swept marine seismic source located in Figure 1 and in [ 0026]-[0032], in it.

[0102] US Application Serial No. 13/327,524, entitled "Seismic Acquisition Using Narrowband Seismic Sources", filed on December 15, 2011, in the name of inventors Joseph A. Dellinger et al., published on June 21, 2012, as US Patent Publication 2012/0155217, and commonly assigned herein for its teachings relating to data acquisition located at [0024]-[0040], [0054]-[ 0059], [0065]-[0088].

[0103] US Application Serial No. 61/894,729, filed October 23, 2013 and US Application Serial No. 14/515,223 filed October 15, 2014, titled " System and Method for Resonator Frequency Control by Active Squeeze Position Feedback", presented on October 23, 2013.

[0104] Other embodiments of the invention will be apparent to those skilled in the art from consideration of the specification and practice of the invention described in this invention. It is intended that the specification and examples be considered as exemplary only, the invention being indicated by the following claims.

Claims (14)

1. A procedure for controlling the trajectory in a resonant marine seismic source (100), comprising: control a frequency of the resonant marine seismic source (100), which includes: estimate a natural frequency of the resonant marine seismic source (100); obtain a frequency error as the difference between the estimated natural frequency of the source and a frequency of the desired trajectory of the resonant marine seismic source (100); and bringing the frequency error to zero, where the frequency of the desired trajectory of the resonant marine seismic source (100) corresponds to a resonance frequency of the resonant marine seismic source (100) when the frequency error is zero; and controlling a movement path of a moving part of an oscillator (105, 130, 132) of the resonant marine seismic source (100) after controlling the frequency of the resonant marine seismic source (100) to be the frequency of the path desired of the resonant marine seismic source, in which the trajectory of movement of the moving part (105, 130, 132) comprises a position, a speed or an acceleration of the moving part of the oscillator, in which the control of the trajectory movement of the moving part (105, 130, 132) includes: detecting the movement path of the moving part of the oscillator (105, 130, 132); derive a motion path error as the difference between a desired motion path of the moving part of the oscillator (105 130, 132) and the detected motion trajectory; and bringing the motion path error to zero, wherein the desired motion path of the moving part of the oscillator (105 130, 132) corresponds to the detected motion path of the moving part of the oscillator (105 130, 132) when the motion trajectory error is zero. 2. The method according to claim 1, wherein estimating the natural frequency of the source includes detecting a parameter associated with the frequency of the source, and wherein bringing the frequency error to zero includes: modifying a frequency control signal to the resonant marine seismic source (100). 3. The method according to claim 1, wherein detecting the motion path includes detecting a parameter of the motion path. 4. The method according to claim 3, wherein bringing the motion path error to zero includes: modify a signal that determines the detected parameter; and iterate control of the trajectory. 5. The method according to claim 1, wherein bringing the motion path error to zero includes: modify a signal that determines the movement path; and iterate control of the trajectory. 6. The method according to claim 1, further comprising performing frequency stabilization control. 7. A resonant marine seismic source (100), comprising: a piston (105, 130, 132) in a sealed housing (170); a solenoid (145, 240) disposed within the fluid-tight housing (170) and connected to a piston (105, 130, 132) which forms part of the fluid-tight housing (170) and which, in operation, resonates at a natural resonant frequency; and a control system (200) arranged within the fluid-tight housing (170) that, in operation, performs: control a frequency of the resonant marine seismic source (100), which includes: estimate a natural frequency of the resonant marine seismic source (100); obtain a frequency error as the difference between the estimated natural frequency of the source and a frequency of the desired trajectory of the resonant marine seismic source (100); and bringing the frequency error to zero, where the frequency of the desired trajectory of the resonant marine seismic source (100) corresponds to a resonance frequency of the resonant marine seismic source (100) when the frequency error is zero; and controlling a movement path of the piston (105, 130, 132) after controlling the frequency of the resonant marine seismic source (100) to be the frequency of the desired path of the resonant marine seismic source, in which the path of Movement of the piston (105, 130, 132) comprises a position, speed or acceleration of the piston, wherein controlling the movement path of the piston (105, 130, 132) includes: detecting the movement path of the piston (105, 130, 132); deriving a motion path error as a difference between a desired motion path of the piston (105,130, 132) and the detected motion path; and bringing the motion path error to zero, wherein the desired motion path of the moving part of the oscillator (105 130, 132) corresponds to the detected motion path of the moving part of the oscillator (105 130, 132) when the motion trajectory error is zero. 8. The resonant marine seismic source (100) according to claim 7, wherein the estimation of the natural frequency of the source includes the detection of a parameter associated with the frequency of the source. 9. The resonant marine seismic source (100) according to claim 8, wherein bringing the frequency error to zero includes: modify a signal that determines the detected parameter; and iterate source frequency control. 10. The resonant marine seismic source (100) according to claim 8, wherein bringing the frequency error to zero includes: modify the excitation signal of the source (100); and iterate source frequency control. 11. The resonant marine seismic source (100) according to claim 7, wherein the detection of the motion path includes the detection of a parameter of the motion path. 12. The resonant marine seismic source (100) according to claim 11, wherein bringing the motion path error to zero includes: modify a signal that determines the detected parameter; and iterate control of the trajectory. 13. The resonant marine seismic source (100) according to claim 7, wherein bringing the motion path error to zero includes: modify a signal that determines the movement path; and iterate control of the trajectory. 14. The resonant marine seismic source (100) according to claim 7, wherein the control system (200) further performs frequency stabilization control.